Previous works have shown that dislocations carry anomalous states in weak topological phases [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}. The label weak indicates that the topological phase is protected by translation symmetry.
The existence of anomalous states at disclinations in the absence of weak topological phases has been shown in Refs. [9]}, [10]}, [11]}, [12]}, [13]}, [14]}.
Moreover, crystalline topological phases generally have a topological response associated with topological lattice defects [11]}.
A possible link between second-order topology and anomalous states at disclinations has been put forward in Refs. [12]}, [14]}.
Furthermore, a correspondence between a fractional corner charge in two-dimensional topological crystalline insulators [18]}, [19]}, [20]}, [21]} and a fractional disclination charge has been shown in Refs. [22]}, [23]}. A correspondence between a topological phase realized on a lattice with dislocations and a topological phase realized on a defect-free lattice on a manifold with a larger genus has been suggested in Refs. [24]}, [25]}, [26]}.
More generally, symmetry-flux defects have been shown to characterize symmetry-protected phases of matter [27]}.
In strongly interacting spin-boson models, it has been suggested that the interplay between spontaneous symmetry breaking and symmetry protected topology leads to the appearence of anomalous defect modes at solitons [28]}, [29]}.
